A week into the ground campaign for Tikrit, Iraqi forces and allied Shi'ite militias continue to clash with Islamic State group militants on the city's outskirts in an attempt to regain territory one outlying town at a time.

The coalition is battling for al-Dour and Albu Ajil, where IS snipers are hampering efforts to clear the towns of the rebel extremists.

Thousands of troops launched Iraq's largest anti-IS offensive last Sunday to reclaim Tikrit, a strategic stronghold between government-controlled Baghdad to the south and Islamic State-held Mosul to the north.

Iraqi forces with tactical help from Iran are carrying out the operation without intervention from the U.S.-led coalition, which continued to bomb IS targets Sunday in Iraq and Syria.

The airstrikes have not supported the Tikrit offensive, but hit 12 other IS positions in Iraq on Sunday, including Mosul, Kirkuk, and Fallujah, as well as in the Syrian border city of Kobani.

The Syrian Observatory for Human Rights reported Sunday that at least 40 Kurdish fighters and Islamic State militants were killed in 24 hours of fierce clashes in the northern Syrian province of Hassakeh.

Baghdad has also requested extra air power from the U.S.-led coalition to protect the country's antiquities, which have been targeted for destruction by Islamic State militants in recent weeks.

Iraq's Tourism and Antiquities Minister Adel Shirshab told reporters, "Our airspace is not in our hands. It's in their hands... I am calling on the international community and coalition to activate its airstrikes and target terrorism wherever it exists."

Also on Sunday, a peshmerga spokesman in Irbil shed more light on the shooting death of a Canadian soldier by friendly fire in northern Iraq last week.

In an interview with the Associated Press, Halgurd Hikmat said special forces Sergeant Andrew Doiron and three other Canadians approached the Kurdish militia on the front lines and responded to questions in Arabic. Peshmerga fighters mistook them for Islamic State forces and opened fire

"The biggest part of the responsibility for this incident lies with them, because they went there without our permission," Hikmat said.